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Question 66
In the given figure, DE$$\parallel$$BC and DE = 1/3 BC. If area of triangle $$ADE = 20 cm^2$$, then what is the area $$(in cm^2)$$ of triangle DEC?Â
Solution
We have :
DE is parallel to BC and DE =BC/3
Now since BC || DE
We can say
ADE is similar to ABC
Now there fore AD:AB =DE:BC =1:3
Also area of ADE : area of ABC = (1/3)^2 =1/9
so we get area of ABC = 180
Now In triangle ABC
CD divides AB in the ratio 1:2
so we get area of BCD : ACD = 2:1
so we get area of ACD = 60
Now therefore area of DEC = 60-20 =40
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